Abstract

A class of finite-dimensional Hopf algebras which generalize the notion of Taft algebras is studied. We give necessary and sufficient conditions for these Hopf algebras to omit a pair in involution. That is, to not have a group-like and a character implementing the square of the antipode. As a consequence, we prove the existence of an infinite set of examples of finite-dimensional Hopf algebras without such pairs. Implications for the theory of anti-Yetter–Drinfeld modules as well as biduality of representations of Hopf algebras are discussed.

中文翻译：

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广义塔夫脱代数和对合对数

摘要

研究了一类推广Taft代数概念的有限维Hopf代数。我们给出了这些 Hopf 代数在对合中省略一对的充要条件。也就是说，没有一个类群和一个实现对极平方的字符。因此，我们证明了没有这些对的有限维 Hopf 代数的无限示例集的存在。讨论了对反Yetter-Drinfeld 模块理论的影响以及Hopf 代数表示的二元性。